The HFLOAT library: fast computations with extreme precision.

The HFLOAT package

The
HUGE-FLOAT package
It's for computations with very long (huge!) floating point numbers.
With hfloat you can compute pi to many million digits.
Latest HFLOAT version:
hfloat-2012.11.17.tgz (approx. 600k),
distributed under the GPL.
hfloat uses fft-multiplication, therefore
you need fxt in order to compile it.
Currently changes happen mostly in fxt,
new hfloat versions are released mainly in order to keep versions in sync.
Please read
whatfor.txt
and
hfloat.lsm
the doc is included, here:
hfdoc.dvi.gz (dvi)
hfdoc.ps.gz (postscript)

A comparison of the implemented algorithms to compute pi:
opcount-64k.txt (precision = 64k digits)
opcount-4M.txt (precision = 4M digits)
It is interesting that the AGM-algorithm
(with Schönhage's optimisations both of the sqrt and the AGM)
needs less than half of the multiplications than
(both variants of) Borwein's 4th order algorithm.

Log about the computation of 9**(9**9), done 22-November-1999
on an AMD K6/2 366Mhz:
run1-pow999.txt.
The computation took almost 8 hours as out of core FFTs had
to be used.
Note added 2010-October-25:
log of a computation that took only 81 seconds
run-pow999-ram.txt.

Some ideas used in hfloat are described in the slides of
my talk "How to compute Pi to 10^12: A crash course in high precision arithmetics"
given October-2003 in Bonn, Germany (gzip compressed):
dvi (35kB),
ps (170kB), or
pdf (200kB).
An updated version, given in Canberra, Australia (in two parts,
April and May 2007) is here:
dvi (36kB),
ps (184kB), or
pdf (204kB).